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几种有理插值函数的逼近性质 总被引:6,自引:1,他引:5
1 引 言在曲线和曲面设计中,样条插值是有用的和强有力的工具.不少作者已经研究了很多种类型的样条插值[1,2,3,4].近些年来,有理插值样条,特别是三次有理插值样条,以及它们在外型控制中的应用,已有了不少工作[5,6,7].有理插值样条的表达式中有某些参数,正是由于这些参数,有理插值样条在外型控制中充分显示了它的灵活性;但也正是由于这些参数,使它的逼近性质的研究增加了困难.因此,关于有理插值样条的逼近性质的研究很少见诸文献.本文在第二节首先叙述几种典型的有理插值样条,其中包括分母为一次、二次的三次有理插值样条和仅基于函数值… 相似文献
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CONSTRAINED RATIONAL CUBIC SPLINE AND ITS APPLICATION 总被引:6,自引:0,他引:6
1. IntroductionDesign of high quality, manufacturable surfaces, such as the outer shape of a ship, car oraeroplane, is an important yet challenging task in today's manufacturing industries. Althoughsignificam progress has been made in the last decade in developing and commercializing pro--duction quality CAD tools, demand for more effective tools is still high due to the ever increajsein model complexity and the needs to address and incorporate manufacturing requirements inthe early stage of … 相似文献
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Robert Schaback 《Constructive Approximation》1990,6(2):167-179
The classical interpolation problems for cubic and rational splines are merged to get an “adaptive” rational interpolating spline which automatically uses cubic pieces to model unavoidable inflection points and retain convexity/concavity elsewhere. An existence proof, a numerical method, and a series of examples are presented. Furthermore, the two-dimensional case is discussed. 相似文献
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Qi Duan Gongxue Xu Aikui Liu Xuefu Wang Fuhua Cheng 《Journal of Applied Mathematics and Computing》1999,6(1):203-215
In this paper, a rational cubic interpolant spline with linear denominator has been constructed, and it is used to constrain interpolation curves to be bounded in the given region. Necessary and sufficient conditions for the interpolant to satisfy the constraint have been developed. The existence conditions are computationally efficient and easy to apply. Finally, the approximation properties have been studied. 相似文献
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Qi Duan Tzer-Shyong Chen K. Djidjeli W. G. Price E. H. Twizell 《Journal of Applied Mathematics and Computing》2000,7(2):397-405
A constrained rational cubic spline with linear denominator was constructed in [1]. In the present paper, the sufficient condition for convex interpolation and some properties in error estimation are given. 相似文献
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加权有理三次插值的逼近性质及其应用 总被引:7,自引:0,他引:7
利用带导数和不带导数的分母为线性的有理三次插值样条构造了一类加权有理三次插值函数,利用这种插值方法,将样条曲线严格约束于给定的折线之上、之下或之间的问题都可以得到解决同时还研究了这种加权有理三次插值的逼近性质。 相似文献
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一种四次有理插值样条及其逼近性质 总被引:3,自引:0,他引:3
1引言有理样条函数是多项式样条函数的一种自然推广,但由于有理样条空间的复杂性,所以有关它的研究成果不象多项式样条那样完美,许多问题还值得进一步的研究.近几十年来,有理插值样条,特别是有理三次有理插值样条,由于它们在曲线曲面设计中的应用,已有许多学者进行了深入研究,取得了一系列的成果(见[1]-[7]).但四次有理插值样条由于其构造所花费的计算量太大以及在使用上很不方便而让人们忽视了其重要的应用价值,因此很少有人研究他们.实际上,在某些情况下四次有理插值样条有其独特的应用效果,如文[8]建立的一种具有局部插值性质的分母为二次的四次有理样条,即一个剖分 相似文献
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Qinghua Sun Fangxun Bao Jianxun Pan Qi Duan 《Mathematical Methods in the Applied Sciences》2013,36(10):1301-1309
A weighted blending interpolator, a kind of smooth rational spline based only on function values, is constructed using a rational cubic spline and a polynomial spline. In order to meet the needs of practical design, a new control method is employed to control the shape of curves. The advantage of the method is that it can be applied to modify the local shape of an interpolating curve by selecting suitable parameters and weight coefficients simply. Also, when the weight coefficient is in [0,1], the error estimation formula of this interpolator is obtained. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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This paper addresses new algorithms for constructing weighted cubic splines that are very effective in interpolation and approximation of sharply changing data. Such spline interpolations are a useful and efficient tool in computer-aided design when control of tension on intervals connecting interpolation points is needed. The error bounds for interpolating weighted splines are obtained. A method for automatic selection of the weights is presented that permits preservation of the monotonicity and convexity of the data. The weighted B-spline basis is also well suited for generation of freeform curves, in the same way as the usual B-splines. By using recurrence relations we derive weighted B-splines and give a three-point local approximation formula that is exact for first-degree polynomials. The resulting curves satisfy the convex hull property, they are piecewise cubics, and the curves can be locally controlled with interval tension in a computationally efficient manner. 相似文献
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《Journal of Computational and Applied Mathematics》1999,102(1):87-117
A scheme is described for interactively modifying the shape of convexity preserving planar interpolating curves. An initial curve is obtained by patching together rational cubic and straight line segments. This scheme has, in general, geometric continuity of order 2(G2 continuity) and preserves the local convexity of the data. A method for interactively modifying such curves, while maintaining their desirable properties, is discussed in detail. In particular, attention is focused upon local changes to the curve, while retaining G2 continuity and shape preserving properties. This is achieved by interactive adjustment of the Bézier control points, followed by automatic adjustment of the values of weights and curvatures in a prescribed manner. A number of examples are presented. 相似文献
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有理B-样条曲线、曲面的包络性质 总被引:1,自引:0,他引:1
研究有理Bezier曲线和B-样条曲线、曲面的包络性质,愈来愈广泛,因为它从包络磨光的角度解释了曲线、曲面的一种几何构造特征,形象地说明了模型是由多边形或多面体逐步磨光的结果. 相似文献
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In the present paper, C1-piecewise rational cubic spline function involving tension parameters is considered which produces a monotonie interpolant
to a given monotonie data set. It is observed that under certain conditions the interpolant preserves the convexity property
of the data set. The existence and uniqueness of a C2-rational cubic spline interpolant are established. The error analysis of the spline interpolant is also given. 相似文献
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The parametric cubic splines interpolating to such closed curves as the circle and ellipse are derived in a form where their parameters are given by simple algebraic expressions. The structure of these expressions enables the error in approximation of the given curves to be precisely determined and some additional features of the spline deduced. 相似文献
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Qi Duan Huanling Zhang Yunfeng Zhang E.H. Twizell 《Journal of Computational and Applied Mathematics》2007
This paper deals with the approximation properties of a kind of rational spline with linear denominator when the function being interpolated is C3 in an interpolating interval. Error estimate expressions of interpolating functions are derived, convergence is established, the optimal error coefficient, ci, is proved to be symmetric about the parameters of the rational interpolation and it is bounded. Finally, the precise jump measurements of the second derivatives of the interpolating function at the knots are given. 相似文献
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Peeter Oja 《BIT Numerical Mathematics》2002,42(4):842-855
For any given data we propose the construction of an interpolating spline of class C
1, which is either a quadratic polynomial or a linear/linear rational function between the knots, and preserves the monotonicity of the data on the sections of rational intervals. We prove the uniqueness and existence of this spline. Numerical tests show good approximation properties and flexibility due to the non-coincidence of the given data arguments and the spline knots which can be chosen freely. 相似文献